Probably Possible

According to Richard Foley (1993),

to say that you believe a proposition is just to say that you are sufficiently confident of its truth for your attitude to be one of belief. Then it is rational for you to believe a proposition just in case it is rational for you to have sufficiently high degree of confidence [or belief] in it, sufficiently high to make your attitude toward it one of belief. (p. 140)

Foley terms the second claim the Lockean Thesis (since a hint of the idea can be found in Locke’s writings). He discusses the thesis in relation to the Preface Paradox and the Lottery Paradox, which, according to him, pose prima facie problems for it. However, I won’t discuss the problems or his proffered solutions. Instead, I shall raise a different worry for the thesis. In a follow-up post, I’ll suggest how to deal with the worry.

Suppose that the threshold that your degree of belief in p has to meet for you to have a belief that p is 0.9. Then, according to Foley, you believe p if, say, your degree of belief in p is 0.95. And it is rational for you to believe p if and only if your degree of belief in p is rational. But there are ostensible cases in which it is not rational for you to believe p, even though it might well be rational for your degree of belief in p to be no less than 0.9. (Ostensible, because I hope to resolve the worry that I raise for the Lockean thesis.) First, consider the following statements:

(1) I’m slightly more confident that B than that A, and I believe that A is equivalent to B.
(2) I’m slightly more confident that Mark Twain wrote Huckleberry Finn than I’m that Samuel Clemens wrote it, and I believe that Mark Twain is Samuel Clemens.
(3) I’m slightly more confident that it’ll rain than that she’ll be late, and I believe that if it rains, she’ll be late.

(1) to (3) sound infelicitous. One is inclined to say, for example, that if you really believe that A is equivalent to B, then you ought to be equally confident in A and in B. One is inclined to say that even if you are just slightly more confident that Mark Twain wrote Huckleberry Finn than that Samuel Clemens wrote it, you ought not believe that Mark Twain is Samuel Clemens. But now consider (4) to (6) below:

(4) I’m slightly more confident that B than that A, and I’m 95% confident that A is equivalent to B.
(5) I’m slightly more confident that Mark Twain wrote Huckleberry Finn than I’m that Samuel Clemens wrote it, and I’m 95% confident that Mark Twain is Samuel Clemens.
(6) I’m slightly more confident that it’ll rain than that she’ll be late, and I’m 95% confident that if it rains, she’ll be late.

(4) to (6) sound quite fine. If you’re absolutely certain that A is equivalent to B, then indeed, you should be as confident in B as you’re in A. But if you’re very, but not absolutely, confident that A and B are equivalent, then you might well be slightly more confident in one than in the other, especially since in the first place, this might be the reason that you’re not certain that they’re equivalent. Indeed, it would be odd to insist that if you’re very, but not absolutely, confident that A is equivalent to B, you ought to be equally confident in A and in B.

(Intuitively, the more confident you are that A is equivalent to B, the less your degree of belief in A should diverge from your degree of belief in B. If you’re extremely confident that A is equivalent to B, you shouldn’t be much more confident in A than you’re in B.)

The above examples pose a problem for the Lockean Thesis, since ostensibly, they show that there are cases in which it is not rational for you to believe p, and yet, it is rational for your degree of belief in p to be as high as it could be - so long as it is not 1. For suppose the threshold that your degree of belief in p has to meet for you to believe p is 1. Replacing `95% confident’ with `100% confident’ in (4) to (6) above will yield statements which sound as bad as (if not worse than) (1) to (3).

Setting the threshold at certainty will get around the worry I raised for the Lockean Thesis. But the claim that belief requires certainty is implausible, as Foley and others have pointed out - just observe the sheer number of beliefs that we hold with less than complete confidence. Also, Foley actually thinks that the Lockean Thesis helps in dealing with the Preface Paradox and the Lottery Paradox, but the prospect for this is dim if to believe p is to be certain that p. So let’s make such a move only if we find other moves lacking.

References:

1. Foley, Richard (1993). Working Without a Net: A Study of Egocentric Epistemology. NY: Oxford University Press.

Posted by wenghong on 3rd May 2007 under Credences, Probability, Rationality. Leave a response?